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I'm defining the functions in the following way 

 ClearAll[Ka, Po, r, P, L, PL];
  params = {r, Po, Ka}
  prmss = ToExpression[StringInsert[Map[ToString, %], "_", -1]]
  eq = {Ka*P*L == PL, Po == P + PL, r*Po == L + PL};
  variables = {P, L, PL};


  sol = Solve[eq, variables] // Last;

 (*Define functoins of variables*)

  Table[variables[[i]][r_, Po_, Ka_] := 
    Evaluate[(variables /. sol)[[i]]], {i, Length[sol]}];  


  Ka = 10000;
  Po = 0.001;


  ParametricPlot[Table[{r, variables[[i]] @@ params}, {i, Length[variables]}], {r, 0.1, 5}]

I would prefer do not list them explicitly like [r_, Po_, Ka_] but to do something like @@prmss

How I can do it in my case?

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1 Answer 1

Reset to default
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Is this what you're after?

ClearAll[f];
params = {r, Po, Ka} // PatternSequence @@ (Pattern[#, Blank[]] & /@ #) &;
f[params] := {r, Po, Ka};
??f

f[PatternSequence[r_,Po_,Ka_]]:={r,Po,Ka}

f[1, 2, 3]

{1, 2, 3}

UPDATE

Per the comments, here's another try.

ClearAll[eq, auto];
SetAttributes[auto, HoldFirst];
auto[eqn_, pvals : ___Rule] :=
 Module[{
   vars = Union@Cases[
      eqn,
      s_Symbol /; 
       StringMatchQ[SymbolName[s], 
        RegularExpression["[A-Z].*"]], \[Infinity]],
   params = Union@Cases[
      eqn,
      s_Symbol /; 
       StringMatchQ[SymbolName[s], 
        RegularExpression["[a-z].*"]], \[Infinity]],
   sol},
  sol = Last[Solve[eqn, vars]];
  With[{
    ilen = Length[vars],
    rrange = {r, .1, 5}},
   ParametricPlot[
    Sequence @@ ({r, #} & /@ (vars /. sol) /. {pvals}), rrange]]]

Then

eq = {ka*P*L == PL, po == P + PL, r*po == L + PL};
auto[eq, po -> .001, ka -> 10000]

resolves to

ParametricPlot[{r,(-1-ka po+ka po r+Sqrt[4 ka po r+(1+ka po-ka po r)^2])/(2 ka)},{r,1/2 (-(1/ka)+po-po r+Sqrt[4 ka po r+(1+ka po-ka po r)^2]/ka)},{r,1/2 (1/ka+po+po r-Sqrt[4 ka po r+(1+ka po-ka po r)^2]/ka)},{r,0.1,5}]

(I left it symbolic here) and generates a plot. This code assumes "variables" start with an uppercase letter and "parameters" start with a lowercase letter. It's just searching for all symbols; you may need to refine that (for example by checking FreeQ[Attributes@s,Protected])

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  • $\begingroup$ Not exactly, but using your code I get two lists: {P[r_, Po_, Ka_], L[r_, Po_, Ka_], PL[r_, Po_, Ka_]} and {-((Po (-1 - Ka + Ka r))/(1 + Ka)), (Po r)/(1 + Ka), (Ka Po r)/( 1 + Ka)}. Now I need to define 3 functions P[r_, Po_, Ka_]:=-((Po (-1 - Ka + Ka r))/(1 + Ka)); L[r_, Po_, Ka_]:=(Po r)/(1 + Ka) and PL[r_, Po_, Ka_]:=(Ka Po r)/( 1 + Ka)}. $\endgroup$
    – Филипп Цветков
    May 27, 2014 at 8:59
  • $\begingroup$ @ФилиппЦветков I think what you are trying to achieve can be done elegantly, but I don't follow exactly what you're seeking. Can you elaborate a bit more on what you want to input and what you want as output? If you have those two lists (call them list1 & list2), you can make definitions with MapThread[SetDelayed, {list1, list2}] $\endgroup$
    – mfvonh
    May 27, 2014 at 14:29
  • $\begingroup$ Yes I did this to make the definitions. My system of equations as well as parameter and variables will be changed. So I would like to avoid they appease in the code explicitly except in the beginning. Thus in input I have the lists of equations, parameters and variables. As soon the system of equation is solved I would like to define the variables as functions of parameters (so parameters becomes variables) to plot system solutions as parameters functions. $\endgroup$
    – Филипп Цветков
    May 27, 2014 at 14:43

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